Problem: Dominic from "Dominic's Pizza" always bakes $p$ pizzas each day. Currently, it costs him $\$10$ per day to use a brick oven and $\$2$ per pizza for the ingredients. One day Dominic realized that if he switched to an electric oven, the use of the oven would cost him $\$20$ per day, but the ingredients would be cheaper, only $\$0.80$ per pizza. This way, his total expenses for each pizza (including shared oven costs and ingredient costs) would be reduced by $\$1$. Write an equation in terms of $p$ to model the situation.
Explanation: The strategy We know that the total expenses per pizza if Dominic uses an electric oven are $1$ less than the total expenses per pizza if Dominic uses a brick oven. If we let $B$ denote the total expenses per pizza using a brick oven and let $E$ denote the total expenses per pizza using an electric oven, we obtain the equation $B=E+1$ Now, let's express $B$ and $E$ in terms of $p$. Expressing the brick oven cost per pizza Using the brick oven, Dominic will pay a flat fee of $\$10$ every day. We know Dominic bakes $p$ pizzas every day, and that if he uses the brick oven, the ingredients cost $\$2$ per pizza. Therefore, $2p$ dollars represents the total cost that Dominic must pay for ingredients every day. Adding this to the $\$10$ flat fee, we see that $10+2p$ dollars represents the total per day cost to bake $p$ pizzas in the brick oven. To find the total expense per pizza, we can divide the total cost by the number of pizzas he makes. So the total expense per pizza when Dominic uses the brick oven is $\:\dfrac{10+2p}{p}$ dollars. Expressing the electric oven cost per pizza Using the electric oven, Dominic will pay a flat fee of $\$20$ every day. If Dominic uses the electric oven, the ingredients cost $\$0.80$ per pizza. Therefore, $0.80p$ dollars represents the total cost that Dominic must pay for ingredients every day. Adding this to the $\$20$ flat fee, we see that $20+0.80p$ dollars represents the total per day cost to bake $p$ pizzas in the electric oven. Therefore, $\:\dfrac{20+0.80p}{p}$ dollars represents the total expenses per pizza when Dominic uses the electric oven. Putting things together We found that $B=\dfrac{10+2p}{p}$ and $E=\dfrac{20+0.80p}{p} $. Since $B=E+1$, we can substitute and find an equation in terms of $p$ that models the situation. The answer is: $ \dfrac{10+2p}{p}=\dfrac{20+0.80p}{p}+1 $